Q: If a right triangle has legs $$a = 44$$ and $$b = 117$$, what is $$\sin(\theta)$$, where $$\theta is $$the angle opposite the side of length $$44$$?

$$\sin(\theta) = \dfrac{44}{125}$$

Q: For the same triangle, what is $$\cos(\theta)$$, where $$\theta is $$the angle opposite the side of length $$44$$?

$$\cos(\theta) = \dfrac{117}{125}$$

Q: What is $$\tan(\theta)$$ for the angle opposite the side of length $$44 in $$the triangle?

$$\tan(\theta) = \dfrac{44}{117}$$

Q: If $$\sin(\theta) = \dfrac{44}{125} in a $$right triangle, what is $$\cos(\theta)$$?

$$\cos(\theta) = \dfrac{117}{125}$$

Question 1

Given a right triangle with legs of length $$a = 44$$ and $$b = 117$$, what is the length of the hypotenuse $$c$$? Use the Pythagorean Theorem.

Accepted Answer

$$c = \sqrt{44^2$ + 117^2$} = 125$$

Question 2

If a right triangle has legs $$a = 44$$ and $$b = 117$$, what is $$\sin(	heta)$$, where $$	heta is $$the angle opposite the side of length $$44$$?

Accepted Answer

$$\sin(	heta) = \dfrac{44}{125}$$

Question 3

For the same triangle, what is $$\cos(	heta)$$, where $$	heta is $$the angle opposite the side of length $$44$$?

Accepted Answer

$$\cos(	heta) = \dfrac{117}{125}$$

Question 4

What is $$	an(	heta)$$ for the angle opposite the side of length $$44 in $$the triangle?

Accepted Answer

$$	an(	heta) = \dfrac{44}{117}$$

Question 5

If the hypotenuse of a right triangle is $$125$$ and one leg is $$44$$, what is the length of the other leg?

Accepted Answer

$$b = \sqrt{125^2$ - 44^2$} = 117$$

Question 6

A ladder is leaning against a wall such that the distance from the ground to the top of the ladder is $$117 ft $$and the base is $$44 ft $$from the wall. What is the length of the ladder?

Accepted Answer

$$\sqrt{44^2$ + 117^2$} = 125 ft$$

Question 7

If $$\sin(	heta) = \dfrac{44}{125} in a $$right triangle, what is $$\cos(	heta)$$?

Accepted Answer

$$\cos(	heta) = \dfrac{117}{125}$$

Question 8

Given a right triangle with sides $$a = 44$$, $$b = 117$$, and $$c = 125$$, what is $$\sin$$^{-1}$$\left(\dfrac{44}{125}\right)$$ approximately in degrees?

Accepted Answer

$$\sin$$^{-1}$$\left(\dfrac{44}{125}\right) \approx 20.7^\circ$$

Question 9

If $$	an(	heta) = \dfrac{44}{117}$$, what is $$	heta in $$degrees (rounded to the nearest tenth)?

Accepted Answer

$$	heta \approx 20.4^\circ$$

Question 10

A surveyor needs to find the height of a building. Standing $$44$$ meters from the base, the angle of elevation to the top is $$	heta$$ such that $$	an(	heta) = \dfrac{117}{44}. $$What is the height of the building?

Accepted Answer

$$117$$ meters

Solving Right Triangles Using the Pythagorean Theorem

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